In 1960, Freeman Dyson proposed how advanced civilizations could create megastructures that enclosed their system, allowing them to harness all of their star's energy and multiplying the habitable space they could occupy. In 2015, the astronomical community was intrigued when the star KIC 8462852 (aka Tabby's Star) began to dim inexplicably. While an analysis of the star's light curve in 2018 revealed that the dimming pattern was more characteristic of dust than a solid structure, Tabby's Star focused attention on the concept of megastructures and their associated technosignatures.
I’d argue that this can’t be an answer for population growth.
We’re already hitting our population leveling off and even shrinking, and that’s economics, not due to resources. Would that apply in general? It has to. Consider the time between filling up a world until being able to build megastructures: thousands of years is optimistic. If a population was constrained by habitable space for thousands of years, they would have had to stop growing, had to have population stability ingrained for many generations. That won’t change easily
I guess a civilization that has the ability to engineer mega structures and move planets could have the sociological knowledge and skill to predict, plan and adjust it’s own population growth. And also humans don’t take up much space. Humanity could be housed in a single massive arcology couple tens of kilometers wide and long and few hundred meters tall with decent living space per head and have room to spare. it’s not the living space but the food, mining, industry, food mostly that takes up area and if that comes an issue there is all kinds of orbital installations that could feed people easier than whipping up a new habitable planet.
I see this rogue planet moving business more like a colonization or vanity project than a solution for population problems.